The deviation of the number variance from the random matrix logarithmic
behavior to a stronger than linear behavior at large energies has been
observed in metallic system [1]}, [2]}.
Recently, it has gained much interest beyond
the traditional single-particle disordered systems. Stronger than linear
deviations of the number variance beyond a certain energy scale have
been seen in the context of
Sachdev-Ye-Kitaev (SYK) model [3]}, [4]},
many body localization systems [5]}, [6]}, [7]}, [8]}
and the generalized Rosenzweig-Porter
random matrix model [9]}, [10]}. In all these cases
it was argued that the energy for which the number variance becomes
stronger than linear corresponds to the inverse of the time scale for which
the motion can no more sample the whole phase space.
